The present invention relates to wireless digital communication systems. More particularly, the present invention relates to producing a system response matrix for such systems.
In code division multiple access communication systems, multiple users send multiple communications simultaneously. The multiple communications are transmitted using different channel codes. The channel codes proposed for the time division duplex mode for 3GPP are derived by combining a spreading code with a scrambling code and subsequently applying a channel code specific multiplier. During transmission, each communication experiences a channel response. One approach to recover data from the transmitted bursts is joint detection, where all users data is received simultaneously. Such a system is shown in FIG. 1. The joint detection receiver may be used in a user equipment or base station.
The multiple communications 20, after experiencing their channel response, are received as a combined received signal at an antenna 22 or antenna array. The received signal is reduced to baseband, such as by a demodulator 24, and sampled at a chip rate of the codes or a multiple of a chip rate of the codes, such as by an analog to digital converter (ADC) 26 or multiple ADCs, to produce a received vector, r. A channel estimation device 28 uses a reference signal, such as a midamble code or pilot code, to estimate the channel response of the communications 20. A joint detection device 30 uses the estimated or known spreading codes of the users' bursts and the estimated or known channel responses to estimate the originally transmitted data for all the users as a data vector, d.
The joint detection problem is typically modeled by Equation 1.Ad+n=r  Equation 1d is the transmitted data vector; r is the received vector; n is the additive white gaussian noise (AWGN); and A is the system response matrix, and is constructed by convolving the channel responses with the known channel codes.
Two approaches to solve Equation 1 is a zero forcing (ZF) and a minimum mean square error (MMSE) approach. A ZF solution, where n is approximated to zero, is per Equation 2.d=(AHA)−1AHr  Equation 2
A MMSE approach is per Equations 3 and 4.d=R−1AHr  Equation 3R=AHA+σ2I  Equation 4σ2 is the variance of the noise, n, and I is the identity matrix.
For either a zero forcing or MMSE solution, the hermetian of the system response matrix, AH, is derived. In the proposed TDD mode of 3GPP, the system response matrix is derived using the spreading codes, the scrambling code, channel code specific multipliers and the determined channel responses. The real spreading code is mixed with a complex scrambling code. The mixed result is multiplied to the channel code specific multipliers (being either real or imaginary) and the result is convolved with the complex channel responses. After the system response matrix is derived, the hermetian is taken to produce the AH matrix. Producing the AH matrix is a complicated operation requiring complex multiplications. Implementing multiplications in hardware is undesirable due to the number of transistors required to produce a multiplier.
Accordingly, it is desirable to have alternate approaches to generate the hermetian of the system response matrix.